comparison src/libvorbis-1.3.3/doc/06-floor0.tex @ 1:05aa0afa9217

Bring in flac, ogg, vorbis

+% -*- mode: latex; TeX-master: "Vorbis_I_spec"; -*-
+%!TEX root = Vorbis_I_spec.tex
+% $Id$
+\section{Floor type 0 setup and decode} \label{vorbis:spec:floor0}
+
+\subsection{Overview}
+
+Vorbis floor type zero uses Line Spectral Pair (LSP, also alternately
+known as Line Spectral Frequency or LSF) representation to encode a
+smooth spectral envelope curve as the frequency response of the LSP
+filter.  This representation is equivalent to a traditional all-pole
+infinite impulse response filter as would be used in linear predictive
+coding; LSP representation may be converted to LPC representation and
+vice-versa.
+
+
+
+\subsection{Floor 0 format}
+
+Floor zero configuration consists of six integer fields and a list of
+VQ codebooks for use in coding/decoding the LSP filter coefficient
+values used by each frame.
+
+\subsubsection{header decode}
+
+Configuration information for instances of floor zero decodes from the
+codec setup header (third packet).  configuration decode proceeds as
+follows:
+
+\begin{Verbatim}[commandchars=\\\{\}]
+  1) [floor0\_order] = read an unsigned integer of 8 bits
+  2) [floor0\_rate] = read an unsigned integer of 16 bits
+  3) [floor0\_bark\_map\_size] = read an unsigned integer of 16 bits
+  4) [floor0\_amplitude\_bits] = read an unsigned integer of six bits
+  5) [floor0\_amplitude\_offset] = read an unsigned integer of eight bits
+  6) [floor0\_number\_of\_books] = read an unsigned integer of four bits and add 1
+  7) array [floor0\_book\_list] = read a list of [floor0\_number\_of\_books] unsigned integers of eight bits each;
+\end{Verbatim}
+
+An end-of-packet condition during any of these bitstream reads renders
+this stream undecodable.  In addition, any element of the array
+\varname{[floor0\_book\_list]} that is greater than the maximum codebook
+number for this bitstream is an error condition that also renders the
+stream undecodable.
+
+
+
+\subsubsection{packet decode} \label{vorbis:spec:floor0-decode}
+
+Extracting a floor0 curve from an audio packet consists of first
+decoding the curve amplitude and \varname{[floor0\_order]} LSP
+coefficient values from the bitstream, and then computing the floor
+curve, which is defined as the frequency response of the decoded LSP
+filter.
+
+Packet decode proceeds as follows:
+\begin{Verbatim}[commandchars=\\\{\}]
+  1) [amplitude] = read an unsigned integer of [floor0\_amplitude\_bits] bits
+  2) if ( [amplitude] is greater than zero ) \{
+       3) [coefficients] is an empty, zero length vector
+       4) [booknumber] = read an unsigned integer of \link{vorbis:spec:ilog}{ilog}( [floor0\_number\_of\_books] ) bits
+       5) if ( [booknumber] is greater than the highest number decode codebook ) then packet is undecodable
+       6) [last] = zero;
+       7) vector [temp\_vector] = read vector from bitstream using codebook number [floor0\_book\_list] element [booknumber] in VQ context.
+       8) add the scalar value [last] to each scalar in vector [temp\_vector]
+       9) [last] = the value of the last scalar in vector [temp\_vector]
+      10) concatenate [temp\_vector] onto the end of the [coefficients] vector
+      11) if (length of vector [coefficients] is less than [floor0\_order], continue at step 6
+
+     \}
+
+ 12) done.
+
+\end{Verbatim}
+
+Take note of the following properties of decode:
+\begin{itemize}
+ \item An \varname{[amplitude]} value of zero must result in a return code that indicates this channel is unused in this frame (the output of the channel will be all-zeroes in synthesis).  Several later stages of decode don't occur for an unused channel.
+ \item An end-of-packet condition during decode should be considered a
+nominal occruence; if end-of-packet is reached during any read
+operation above, floor decode is to return 'unused' status as if the
+\varname{[amplitude]} value had read zero at the beginning of decode.
+
+ \item The book number used for decode
+can, in fact, be stored in the bitstream in \link{vorbis:spec:ilog}{ilog}( \varname{[floor0\_number\_of\_books]} -
+1 ) bits.  Nevertheless, the above specification is correct and values
+greater than the maximum possible book value are reserved.
+
+ \item The number of scalars read into the vector \varname{[coefficients]}
+may be greater than \varname{[floor0\_order]}, the number actually
+required for curve computation.  For example, if the VQ codebook used
+for the floor currently being decoded has a
+\varname{[codebook\_dimensions]} value of three and
+\varname{[floor0\_order]} is ten, the only way to fill all the needed
+scalars in \varname{[coefficients]} is to to read a total of twelve
+scalars as four vectors of three scalars each.  This is not an error
+condition, and care must be taken not to allow a buffer overflow in
+decode. The extra values are not used and may be ignored or discarded.
+\end{itemize}
+
+
+
+
+\subsubsection{curve computation} \label{vorbis:spec:floor0-synth}
+
+Given an \varname{[amplitude]} integer and \varname{[coefficients]}
+vector from packet decode as well as the [floor0\_order],
+[floor0\_rate], [floor0\_bark\_map\_size], [floor0\_amplitude\_bits] and
+[floor0\_amplitude\_offset] values from floor setup, and an output
+vector size \varname{[n]} specified by the decode process, we compute a
+floor output vector.
+
+If the value \varname{[amplitude]} is zero, the return value is a
+length \varname{[n]} vector with all-zero scalars.  Otherwise, begin by
+assuming the following definitions for the given vector to be
+synthesized:
+
+   \begin{displaymath}
+     \mathrm{map}_i = \left\{
+       \begin{array}{ll}
+          \min (
+            \mathtt{floor0\texttt{\_}bark\texttt{\_}map\texttt{\_}size} - 1,
+            foobar
+          ) & \textrm{for } i \in [0,n-1] \\
+          -1 & \textrm{for } i = n
+        \end{array}
+      \right.
+    \end{displaymath}
+
+    where
+
+    \begin{displaymath}
+    foobar =
+      \left\lfloor
+        \mathrm{bark}\left(\frac{\mathtt{floor0\texttt{\_}rate} \cdot i}{2n}\right) \cdot \frac{\mathtt{floor0\texttt{\_}bark\texttt{\_}map\texttt{\_}size}} {\mathrm{bark}(.5 \cdot \mathtt{floor0\texttt{\_}rate})}
+      \right\rfloor
+    \end{displaymath}
+
+    and
+
+    \begin{displaymath}
+      \mathrm{bark}(x) = 13.1 \arctan (.00074x) + 2.24 \arctan (.0000000185x^2 + .0001x)
+    \end{displaymath}
+
+The above is used to synthesize the LSP curve on a Bark-scale frequency
+axis, then map the result to a linear-scale frequency axis.
+Similarly, the below calculation synthesizes the output LSP curve \varname{[output]} on a log
+(dB) amplitude scale, mapping it to linear amplitude in the last step:
+
+\begin{enumerate}
+ \item  \varname{[i]} = 0
+ \item  \varname{[$\omega$]} = $\pi$ * map element \varname{[i]} / \varname{[floor0\_bark\_map\_size]}
+ \item if ( \varname{[floor0\_order]} is odd ) {
+  \begin{enumerate}
+   \item calculate \varname{[p]} and \varname{[q]} according to:
+           \begin{eqnarray*}
+             p & = & (1 - \cos^2\omega)\prod_{j=0}^{\frac{\mathtt{floor0\texttt{\_}order}-3}{2}} 4 (\cos([\mathtt{coefficients}]_{2j+1}) - \cos \omega)^2 \\
+             q & = & \frac{1}{4} \prod_{j=0}^{\frac{\mathtt{floor0\texttt{\_}order}-1}{2}} 4 (\cos([\mathtt{coefficients}]_{2j}) - \cos \omega)^2
+           \end{eqnarray*}
+
+  \end{enumerate}
+  } else \varname{[floor0\_order]} is even {
+  \begin{enumerate}[resume]
+   \item calculate \varname{[p]} and \varname{[q]} according to:
+           \begin{eqnarray*}
+             p & = & \frac{(1 - \cos\omega)}{2} \prod_{j=0}^{\frac{\mathtt{floor0\texttt{\_}order}-2}{2}} 4 (\cos([\mathtt{coefficients}]_{2j+1}) - \cos \omega)^2 \\
+             q & = & \frac{(1 + \cos\omega)}{2} \prod_{j=0}^{\frac{\mathtt{floor0\texttt{\_}order}-2}{2}} 4 (\cos([\mathtt{coefficients}]_{2j}) - \cos \omega)^2
+           \end{eqnarray*}
+
+  \end{enumerate}
+  }
+
+ \item calculate \varname{[linear\_floor\_value]} according to:
+         \begin{displaymath}
+           \exp \left( .11512925 \left(\frac{\mathtt{amplitude} \cdot \mathtt{floor0\texttt{\_}amplitute\texttt{\_}offset}}{(2^{\mathtt{floor0\texttt{\_}amplitude\texttt{\_}bits}}-1)\sqrt{p+q}}
+                  - \mathtt{floor0\texttt{\_}amplitude\texttt{\_}offset} \right) \right)
+         \end{displaymath}
+
+ \item \varname{[iteration\_condition]} = map element \varname{[i]}
+ \item \varname{[output]} element \varname{[i]} = \varname{[linear\_floor\_value]}
+ \item increment \varname{[i]}
+ \item if ( map element \varname{[i]} is equal to \varname{[iteration\_condition]} ) continue at step 5
+ \item if ( \varname{[i]} is less than \varname{[n]} ) continue at step 2
+ \item done
+\end{enumerate}
+
+
+
+
+
+
+